In a cartesian bicategoryB\mathbf{B}, the pair of terms diagonal, codiagonal refer to the canonical comultiplication Δ:X→X⊗X\Delta: X \to X \otimes X and the dual multiplication ∇=Δ*:X⊗X→X\nabla = \Delta_*: X \otimes X \to X on any object. While the comultiplication is not a true diagonal (because ⊗\otimes is not a cartesian product in B\mathbf{B}), it is the diagonal when seen as belonging to the subcategory of maps (left adjoints), where the restriction of ⊗\otimes to Map(B)Map(\mathbf{B}) becomes a 2-product. Similarly, ∇\nabla is not a true codiagonal on B\mathbf{B}, but it becomes a codiagonal in the sense above when seen as belonging to Map(B)opMap(\mathbf{B})^{op}, the opposite obtained by reversing 11-cells but not 22-cells.